Mathematics

# Evaluate : $\displaystyle \int \left[e^{(2-5x)}+\frac{2}{6x+1}\right]dx$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
The value of $\cfrac { \int _{ 0 }^{ \pi /2 }{ { \left( \sin { x } \right) }^{ \sqrt { 3 } +1 } } dx }{ \int _{ 0 }^{ \pi /2 }{ { \left( \sin { x } \right) }^{ \sqrt { 3 } -1 } } }$ is
• A. $\cfrac { \sqrt { 3 } -1 }{ \sqrt { 3 } +1 }$
• B. $\cfrac { \sqrt { 3 } +1 }{ \sqrt { 3 } }$
• C. $\cfrac { 3-\sqrt { 3 } }{ 2 }$
• D. $\cfrac { \sqrt { 3 } +1 }{ \sqrt { 3 } -1 }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int \frac{1}{e^{x}+1}dx.$
• A. $\displaystyle x-\log \left ( e^{x} -1\right ).$
• B. $\displaystyle x+\log \left ( e^{x} +1\right ).$
• C. $\displaystyle \log \left ( e^{x} +1\right ).$
• D. $\displaystyle x-\log \left ( e^{x} +1\right ).$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate : $\displaystyle \int e^x \cdot \frac {x}{(1+x)^2}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
If $f\left(\displaystyle\frac{3x-4}{3x+4}\right)=x+2, x\neq -\displaystyle\frac{4}{3}$, and $\displaystyle\int f(x)dx=A\log |1-x|+Bx+C$, then the ordered pair $(A, B)$ is equal to (where C is a constant of integration)
• A. $\left(\displaystyle\frac{8}{3}, \frac{2}{3}\right)$
• B. $\left(\displaystyle -\frac{8}{3}, -\frac{2}{3}\right)$
• C. $\left(\displaystyle\frac{8}{3}, -\frac{2}{3}\right)$
• D. $\left(\displaystyle -\frac{8}{3}, \frac{2}{3}\right)$

$\int \sin ^3x\cos^3xdx$